Friday, November 3, 2017

Season 10, stage 1 qualifying simulation after round 20

I reran the simulation almost at the end of round 20, only the last Wasp-Gull game is still running. There are 4 more known
results that don't have to be simulated. The full explanation of how the
simulation is run can be found in my previous post.

This is the last simulation I'll run this stage. The results are getting clear and the probabilities are not necessary. My analysis can be found here.

Gull and Fire continue to lead the qualification predictions, over 90% of simulations without need of a tiebreak. The Booot - Chiron game ended in a draw, Booot has improved its chances while Chiron is now worse. Fizbo has a small chance of reaching a tie break.

The remaining games

Fire (13 pts) - 1 Hard, 2 Easy, 0 Within

Booot (13 pts) - 1 Hard, 0 Easy, 2 Within (Jonny, Hannibal)

Gull (12.5 pts) - 1 Hard, 3 Easy, 0 Within

Chiron (11.5 pts) - 0 Hard, 3 Easy, 0 Within

Fizbo (11.5 pts) - 1 Hard, 2 Easy, 0 Within

Hannibal (10.5 pts) - 1 Hard, 1 Easy, 1 Within (Booot)

Jonny (10.5 pts) - 0 Hard, 2 Easy, 1 Within (Booot)

Note that Hannibal and Jonny are out of the race with very high probability, so the special effect of the remaining "within" games is irrelevant.

Results of 10000 simulationsAverage final scores, sorted:

Gull - 15.03515

Fire - 14.77820

Booot - 14.28420

Chiron - 13.76800

Fizbo - 13.28110

Jonny - 12.50370

Hannibal - 12.01775

Percent of simulations to qualify, including tie breaks:

(without tie break) + (need tie break)

Gull - 93% + 5%

Fire - 90% + 8%

Booot - 60% + 23%

Chiron - 18% + 26%

Fizbo - 2% + 11%

Jonny - 0% + 2%

Hannibal - 0% + 0%

Score for 3rd place including tie breaks:

13 or less - less than 1%

13.5 - 9%

14 - 41%

14.5 - 41%

15 or more - 9%

Tie break combinations

31% of the simulations
require a tie break, which could be at least 4 for first place, at
least 3 for second, or at least 2 for third. There are many possible
combinations of engines that require a tie break, the five most common
ones are

Booot / Chiron - 10.7%

Fire / Chiron - 2.9%

Booot / Chiron / Fizbo - 2.7%

Booot / Fizbo - 2.4%

Fire / Booot / Chiron - 1.9%

Score-qualification graphs

A breakdown of qualification by score for Chiron, Booot, Fire and Fizbo: